>> I already envisioned such request
>
> All right.  Just for the record, this would be useful to create a
> context menu for images.

The patch below will allow using the text property like

  'context-menu-functions '(image-context-menu)

> Also, I could take advantage of it to slightly
> simplify the context menu of jit-spell.

Actually, flyspell was the reason why the text property
`context-menu-function' overrides everything:

1. `make-flyspell-overlay' puts an overlay property

   (overlay-put overlay 'context-menu-function 'flyspell-context-menu)

2. `flyspell-context-menu' returns `flyspell-correct-word'

3. `context-menu-map' should return this symbol unmodified

4. at the end, the symbol `flyspell-correct-word' is executed
   as a command from the menu binding in `context-menu-entry'
   or from `context-menu-open':

    (if (commandp map)
        (call-interactively map)